Answer:
Coordinates of Q [tex](x_2,y_2) \:are\: \mathbf{(7,16)}[/tex]
Option D is correct option.
Step-by-step explanation:
We are given:
K is the midpoint of PQ
Coordinates of P = (-9,-4)
Coordinates of K = (-1,6)
We need to find coordinates of Q [tex](x_2,y_2)[/tex]
We will use the formula of midpoint: [tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
We are given midpoint K and [tex]x_1,y_1[/tex] the coordinates of P we need to find [tex]x_2,y_2[/tex] the coordinates of Q.
[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\(-1,6)=(\frac{-9+x_2}{2},\frac{-4+y_2}{2})\\[/tex]
Now, we can write
[tex]-1=\frac{-9+x_2}{2}, 6=\frac{-4+y_2}{2}\\Simplifying:\\-2=-9+x_2\:,\: 12=-4+y_2\\-2+9=x_2\:,\: 12+4=+y_2\\x_2=7\:,\:y_2=16[/tex]
So, we get coordinates of Q [tex](x_2,y_2) \:are\: \mathbf{(7,16)}[/tex]
Option D is correct option.
